Solve (4a^4b^6/8b^2)^3

$$( \frac { 4 a ^ { 4 } b ^ { 6 } } { 8 b ^ { 2 } } ) ^ { 3 }$$

Evaluate

$$\frac{\left(ab\right)^{12}}{8}$$

Solution Steps

Cancel out 4b^{2} in both numerator and denominator.

$$\left(\frac{a^{4}b^{4}}{2}\right)^{3}$$

To raise \frac{a^{4}b^{4}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(a^{4}b^{4}\right)^{3}}{2^{3}}$$

Expand \left(a^{4}b^{4}\right)^{3}.

$$\frac{\left(a^{4}\right)^{3}\left(b^{4}\right)^{3}}{2^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{a^{12}\left(b^{4}\right)^{3}}{2^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{a^{12}b^{12}}{2^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{a^{12}b^{12}}{8}$$

Expand

$$\frac{\left(ab\right)^{12}}{8}$$

Solution Steps

Cancel out 4b^{2} in both numerator and denominator.

$$\left(\frac{a^{4}b^{4}}{2}\right)^{3}$$

To raise \frac{a^{4}b^{4}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(a^{4}b^{4}\right)^{3}}{2^{3}}$$

Expand \left(a^{4}b^{4}\right)^{3}.

$$\frac{\left(a^{4}\right)^{3}\left(b^{4}\right)^{3}}{2^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{a^{12}\left(b^{4}\right)^{3}}{2^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{a^{12}b^{12}}{2^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{a^{12}b^{12}}{8}$$